/*							fresnl.c
 *
 *	Fresnel integral
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, S, C;
 * void fresnl();
 *
 * fresnl( x, _&S, _&C );
 *
 *
 * DESCRIPTION:
 *
 * Evaluates the Fresnel integrals
 *
 *           x
 *           -
 *          | |
 * C(x) =   |   cos(pi/2 t**2) dt,
 *        | |
 *         -
 *          0
 *
 *           x
 *           -
 *          | |
 * S(x) =   |   sin(pi/2 t**2) dt.
 *        | |
 *         -
 *          0
 *
 *
 * The integrals are evaluated by a power series for x < 1.
 * For x >= 1 auxiliary functions f(x) and g(x) are employed
 * such that
 *
 * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
 * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
 *
 *
 *
 * ACCURACY:
 *
 *  Relative error.
 *
 * Arithmetic  function   domain     # trials      peak         rms
 *   IEEE       S(x)      0, 10       10000       2.0e-15     3.2e-16
 *   IEEE       C(x)      0, 10       10000       1.8e-15     3.3e-16
 *   DEC        S(x)      0, 10        6000       2.2e-16     3.9e-17
 *   DEC        C(x)      0, 10        5000       2.3e-16     3.9e-17
 */

 /*
 Cephes Math Library Release 2.8:  June, 2000
 Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
 */

#include "const.h"
#include "polevl.h"
#include <math.h>


 /* S(x) for small x */
static double sn[6] = {
    -2.99181919401019853726E3,
     7.08840045257738576863E5,
    -6.29741486205862506537E7,
     2.54890880573376359104E9,
    -4.42979518059697779103E10,
     3.18016297876567817986E11,
};
static double sd[6] = {
    /* 1.00000000000000000000E0,*/
     2.81376268889994315696E2,
     4.55847810806532581675E4,
     5.17343888770096400730E6,
     4.19320245898111231129E8,
     2.24411795645340920940E10,
     6.07366389490084639049E11,
};

/* C(x) for small x */
static double cn[6] = {
    -4.98843114573573548651E-8,
     9.50428062829859605134E-6,
    -6.45191435683965050962E-4,
     1.88843319396703850064E-2,
    -2.05525900955013891793E-1,
     9.99999999999999998822E-1,
};
static double cd[7] = {
     3.99982968972495980367E-12,
     9.15439215774657478799E-10,
     1.25001862479598821474E-7,
     1.22262789024179030997E-5,
     8.68029542941784300606E-4,
     4.12142090722199792936E-2,
     1.00000000000000000118E0,
};

/* Auxiliary function f(x) */
static double fn[10] = {
      4.21543555043677546506E-1,
      1.43407919780758885261E-1,
      1.15220955073585758835E-2,
      3.45017939782574027900E-4,
      4.63613749287867322088E-6,
      3.05568983790257605827E-8,
      1.02304514164907233465E-10,
      1.72010743268161828879E-13,
      1.34283276233062758925E-16,
      3.76329711269987889006E-20,
};
static double fd[10] = {
      7.51586398353378947175E-1,
      1.16888925859191382142E-1,
      6.44051526508858611005E-3,
      1.55934409164153020873E-4,
      1.84627567348930545870E-6,
      1.12699224763999035261E-8,
      3.60140029589371370404E-11,
      5.88754533621578410010E-14,
      4.52001434074129701496E-17,
      1.25443237090011264384E-20,
};

/* Auxiliary function g(x) */
static double gn[11] = {
      5.04442073643383265887E-1,
      1.97102833525523411709E-1,
      1.87648584092575249293E-2,
      6.84079380915393090172E-4,
      1.15138826111884280931E-5,
      9.82852443688422223854E-8,
      4.45344415861750144738E-10,
      1.08268041139020870318E-12,
      1.37555460633261799868E-15,
      8.36354435630677421531E-19,
      1.86958710162783235106E-22,
};
static double gd[11] = {
      1.47495759925128324529E0,
      3.37748989120019970451E-1,
      2.53603741420338795122E-2,
      8.14679107184306179049E-4,
      1.27545075667729118702E-5,
      1.04314589657571990585E-7,
      4.60680728146520428211E-10,
      1.10273215066240270757E-12,
      1.38796531259578871258E-15,
      8.39158816283118707363E-19,
      1.86958710162783236342E-22,
};

int fresnl(double xxa, double *ssa, double *cca)
{
    double f, g, cc, ss, c, s, t, u;
    double x, x2;

    x = fabs(xxa);
    x2 = x * x;

    if (x2 < 2.5625)
    {
        t = x2 * x2;
        ss = x * x2 * polevl(t, sn, 5) / p1evl(t, sd, 6);
        cc = x * polevl(t, cn, 5) / polevl(t, cd, 6);
        goto done;
    }

    if (x > 36974.0)
    {
        cc = 0.5;
        ss = 0.5;
        goto done;
    }

    /*		Asymptotic power series auxiliary functions
     *		for large argument
     */
    x2 = x * x;
    t = FULL_PI_FRESNEL * x2;
    u = 1.0 / (t * t);
    t = 1.0 / t;
    f = 1.0 - u * polevl(u, fn, 9) / p1evl(u, fd, 10);
    g = t * polevl(u, gn, 10) / p1evl(u, gd, 11);

    t = HALF_PI_FRESNEL * x2;
    c = cos(t);
    s = sin(t);
    t = FULL_PI_FRESNEL * x;
    cc = 0.5 + (f * s - g * c) / t;
    ss = 0.5 - (f * c + g * s) / t;

done:
    if (xxa < 0.0)
    {
        cc = -cc;
        ss = -ss;
    }

    *cca = cc;
    *ssa = ss;
    return(0);
}
